Write the logarithmic form of the Arrhenius equation $k = A e^{-\frac{E_a}{RT}}$.
(N/A) The Arrhenius equation is given by: $k = A e^{-\frac{E_a}{RT}}$
Taking the natural logarithm $(\ln)$ on both sides:
$\ln k = \ln(A e^{-\frac{E_a}{RT}})$
Using the logarithmic property $\ln(xy) = \ln x + \ln y$:
$\ln k = \ln A + \ln(e^{-\frac{E_a}{RT}})$
Since $\ln(e^x) = x$,we get:
$\ln k = \ln A - \frac{E_a}{RT}$
Alternatively,converting to base $10$ logarithm $(\log_{10})$:
$\log_{10} k = \log_{10} A - \frac{E_a}{2.303 RT}$
Taking the natural logarithm $(\ln)$ on both sides:
$\ln k = \ln(A e^{-\frac{E_a}{RT}})$
Using the logarithmic property $\ln(xy) = \ln x + \ln y$:
$\ln k = \ln A + \ln(e^{-\frac{E_a}{RT}})$
Since $\ln(e^x) = x$,we get:
$\ln k = \ln A - \frac{E_a}{RT}$
Alternatively,converting to base $10$ logarithm $(\log_{10})$:
$\log_{10} k = \log_{10} A - \frac{E_a}{2.303 RT}$
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